Sensors and Actuators A 284 (2018) 158–167

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Sensors and Actuators A: Physicaljournal homepage: www.elsevier.com/locate/sna

Ultrasonic motors with poly phenylene sulﬁde/alumina/PZT
triple-layered vibrators
Jiang Wu ∗ , Yosuke Mizuno, Kentaro Nakamura
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology, Yokohama 226-8503, Japana r t i c l e

i n f oArticle history:
Received 28 July 2018
Received in revised form 8 September 2018
Accepted 26 September 2018
Available online 4 October 2018
Keywords:
Ultrasonic motors
Vibrators
Triple layer
Alumina
Poly phenylene sulﬁdea b s t r a c t
Our previously reported ultrasonic motors with poly phenylene sulﬁde (PPS)/lead zirconate titanate (PZT)
double-layered vibrators were capable of providing high rotation speeds and light weight, but their output torques and power were limited owing to the low stiffness of PPS vibrating bodies. In this study, weconstructed a triple-layered vibrator by sandwiching a thin alumina disk between the PPS vibrating bodyand PZT disk to compensate the stiffness. First, their fundamental vibration characteristics were investigated as some of key dimensions were varied. The force factor of the PPS/alumina/PZT triple-layered
vibrator reached the maximal value when the neutral axis located at the boundary between the PZT andalumina disks. In contrast, the neutral axes existed in the PZT disks for the PPS/PZT double-layered vibrators; this caused the relatively low force factors compared to the triple-layered vibrators. Subsequently,
the load characteristics of the PPS/alumina/PZT triple-layered motors were experimentally assessed. The
maximum output torque and power of the triple-layered motors were 5 and 13 times the values of the
double-layered motors, respectively, owing to the enhanced force factor and electromechanical coupling
factor. Besides, the optimal thickness was lower for the triple- than for the double-layered motor. Theseadvantages indicate the potential of our newly designed triple-layered motors for practical applications.
© 2018 Elsevier B.V. All rights reserved.

1. Introduction
Ultrasonic motors (USMs) exhibit high output torques at low
rotational speeds [1,2], simple structures [3], and fast responses[4,5]. Currently, they have some special applications, e.g. auto-focus
lenses in digital cameras or optical instruments [6,7]. Recently,
USMs capable of working in acid or alkaline environments havebecome increasingly demanded as potential key actuators of robots
for the chemical industry [8,9]. However, the current USMs areinapplicable as most of their vibrators, which are core componentsof USMs, are made of stainless steel or aluminum alloy. In previous studies [10–15], we bonded vibrating bodies made of poly
phenylene sulﬁde (PPS), a functional polymer with low mechanical loss [10,11], on lead zirconate titanate (PZT) disks to form
double-layered motors. They provided high rotation speeds andlight weight but limited output torques and power due to thelow stiffness of the polymer parts [14]. Utilization of rigid ceramics would be a possible method of enhancing the stiffness [16].
However, our recent study [17] found that the vibrator of which
the entire vibrating body was made of rigid ceramics easily frac-∗ Corresponding author.
E-mail address: wujiang@sonic.pi.titech.ac.jp (J. Wu).
https://doi.org/10.1016/j.sna.2018.09.069
0924-4247/© 2018 Elsevier B.V. All rights reserved.

tured even at a low voltage as it exhibited extremely large stressdue to the high stiffness. As a consequence, this motor did havethe capability to provide a good performance. To overcome thesedrawbacks, in this study, we develop a new vibrator with a triplelayered structure: A thin disk made of rigid ceramics is sandwiched
between the PPS vibrating body and PZT disk; using this structure,
the stiffness can be adjusted by changing the dimensions of eachlayer. To date, several triple-layered (or multi-layered) vibrators
for USMs have been reported. Thin ﬁlms, typically made of nitrides
and oxides, were coated on metal vibrating bodies to improve thefrictional and/or abrasional properties [18–20]. But these studies
did not focus on the vibration characteristics. Actually, the ﬁlms
were too thin to affect the vibration characteristics. Recently, Li
et al. have bonded metal/polymer-matrix materials on metal plates
to form multi-layered vibrators [21], of which the matrix-material
layers have the thicknesses comparable to the metal layers, andanalyzed how the material constants and dimensions affect the frictional loss. However, how the motor properties, e.g. the ellipticalmotion shapes, force factors, and load characteristics, depended
on the geometrical parameters were not discussed. It is necessary to systemically investigate these dependences for structural
optimization.
In this study, ﬁrst, we preliminarily select the suitable ceramic(s)as the middle layer by measuring the damping coefﬁcients of

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159

Fig. 1. Schematics of (a) PPS/PZT double-layered and (b) PPS/rigid-ceramic/PZT
triple-layered vibrators.

several functional rigid ceramics. Subsequently, we analyze theelliptical motion shapes and the force factors of triple-layered
vibrators as the thicknesses of the PPS vibrating bodies and therigid ceramic layers are varied. Finally, we measure the load characteristics of the motors with triple-layered vibrators. As the ﬁrst
report regarding the PPS/alumina/PZT triple-layered motors, thispaper focuses on the load characteristics as they are the fundamental performance for USMs [1,2]. Other performance, such as motion
precision, will be explored in our further studies.
2. Triple-layered vibrator
2.1. Basic conﬁguration
Fig. 1(a) and (b) illustrate the conﬁgurations of the double- andtriple-layered vibrators, respectively. In the previous design, a PPS
vibrating body with periodical slots is directly bonded on a thin
PZT disk. The slotted upper surface contacts the rotor and generate frictional force. The ceramic disk is sandwiched between the
PPS vibrating body and the PZT disk in the new design. The threebodies are bonded ﬁrmly with epoxy resin to achieve high reliability of this motor. Since the ceramic disk has a simple shape, there
exists almost no difference in the structural complexity between
the triple- and double-layered vibrators.
2.2. Selection of middle layer
To date, there have been no reports regarding the mechanicaldamping coefﬁcients of rigid ceramics at several tens of kilohertz[10,11]. Thus, prior to evaluation of triple-layered vibrators, thedamping coefﬁcients were measured via the impact method toFig. 2. Experimental setup for measuring the damping coefﬁcients of the tested
rigid ceramics.

select suitable one(s) as the middle layer [10,12]. Alumina, steatite,silicon carbide, and aluminum nitride are tested as they have wideindustrial applications [16]. Their material constants are listed inTable 1. Fig. 2 schematically illustrates the experimental setup. Several rectangular plates 50 mm in length, 10 mm in width, and 1 mm
in thickness were prepared, and one end of them was tightly ﬁxed
with a screw. We hammered the middle part of the plate to apply
an impulse mechanical input, and measured the vibration velocities of the free end with an out-of-plane laser Doppler vibrometer(NLV1232, Polytec, Waldbronn, Germany). The vibration velocityy(t) is theoretically expressed asy(t) = A exp −ˇωt sin (ωt + ϑ) ,(1)

where 2ˇ, ω, A, and ϑ are the damping coefﬁcient, angular frequency, initial amplitude, and phase, respectively. Fig. 3(a) and (b)show the damped oscillation of the alumina plate and an exponential ﬁtting of the envelope, and the response in frequency
domain, respectively. The results shown in Fig. 3 demonstrate thatˇω = 11.82 and ω = 42,454 rad/s. Therefore, the damping coefﬁcient2ˇ is 0.0005. For each sample, the damping coefﬁcients are measured for 20 times and the average values are indicated in Fig. 4.
Silicon carbide exhibits a damping coefﬁcient of 0.0006, comparable to the value of alumina. However, the silicon carbide samples
easily fractured in our experiments; this is assumed to be causedby the fragility [22]. Thus, alumina is employed as the middle layer
in our trial.

Fig. 3. (a) Damped oscillation of alumina plate under an impulse mechanical input and (b) its response in frequency domain.

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J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

Table 1
Mechanical constants of polymers and ceramics.
Materials
Polymer
Ceramics

PPS
Alumina (Al2 O3 )Steatite (3MgO·4SiO2 ·H2 O)
Silicon carbide (SiC)
Aluminum nitride (AlN)

Density/×103 kg/m3

Elastic modulus/GPa

Poisson’s ratio

1.35
3.90
2.80
3.10
3.30

3.45
390
120
410
320

0.36
0.23
0.22
0.16
0.24

3.2. Principle
When sinusoidal voltages sin(ω0 t), cos(ω0 t), –sin(ω0 t), and–cos(ω0 t), where ω0 denotes the resonance frequency, are applied
to the electrodes I, V, and IX; II, VI, and X; III, VII, and XI; and IV, VIII,
and XII; respectively, as shown in Fig. 5(b), two standing waves inthe 3rd bending modes:





 



 

u1 t,  = U sin (ω0 t) sin k
and



(2)

u2 t,  = U cos (ω0 t) cos k

Fig. 4. Measured damping coefﬁcients of alumina, steatite, silicon carbide, and aluminum nitride.

(3)

are excited. Here, , U, and k denote the circumferential angle, vibration amplitude, and wave number (k = 3), respectively. A travelingwave is formed by the superposition of these standing waves:

uz t,  =

2









ui t,  = U cos ω0 t − k .

(4)

i=1

3. Vibration characteristics of triple-layered vibrators
3.1. Practical design of triple-layered vibrator
Fig. 5(a) detailedly illustrates the structure and dimensions of
the triple-layered vibrator. The PPS vibrating body had a cylindricalpart 20 and 30 mm in inner and outer diameters, respectively, and abottom disk 0.5 mm in thickness. Radial slots 0.5 mm in width and
4 mm in depth were created on the cylindrical part with an interval of 10◦ . A polar coordinate (z, r, and  axes) is established on the
top surface. The PZT disk (C213, Fuji Ceramics, Fujinomiya, Japan)
had inner and outer diameters of 20 and 30 mm, respectively, anda thickness of 0.5 mm. As shown in Fig. 5(b), the bottom surface of
the PZT disk was evenly divided into 12 parts (I–XII). The opposite
side without division was bonded to one side of the alumina annular disk, of which the inner and outer diameters were respectively
identical to those of the PZT disk. The other side of the alumina
disk was glued to the bottom surface of the PPS vibrating body. The
ceramic disk thickness s and the un-slotted part thickness t of the
PPS vibrating body are varied in this study.

In ﬂexural vibration, the -axis vibration velocity is derived from
uz :







u t,  = −ς ·∂uz t, 
∂







= ς kU sin ω0 t − k ,(5)where ς is a ratio determined by the vibrator structure and thevibration mode. Thus,uz t, 
U

 2


+



u t, 

ς kU

 2
= 1.

(6)

The elliptical motion drives the rotor pressed to its upper surface
via frictional force. Along the r axis, there also exist vibration components, which have 180◦ phase differences with those along thez axis. Thus, the trajectories in the z-r planes are lines. The elliptical motion shapes, indicated by the ratios v /vz (=ς k) and vr /vz ,greatly affect the motor performance [1,2,14,15]. Here, vz and vr
are respectively the vertical and radial vibration velocities at antinodes, and v is the circumferential vibration velocity at nodes. The

Fig. 5. Triple-layered vibrator. (a) Conﬁguration and dimensions, where h, t, s, p, and b represent the height of the slotted part (4 mm), the thickness of the un-slotted partof the PPS vibrating body, the thickness of the alumina disk, the thickness of the PZT disk (0.5 mm), and the radial thickness (5 mm), respectively. (b) the PZT disk and thevoltage applied to each electrode. (c) The 3rd bending vibration mode.

J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

161

impedance analyzer (4294 A, Agilent, Santa Clara, CA, USA)] using
the following equations:2f0 · Q
1
=
,
Cm
Ym0

(7)

Q
,
2f0 · Ym0

(8)

1
.
Ym0

(9)

Lm =
and
Rm =

Fig. 6. Resonance frequencies of the 3rd order bending mode as functions of the
thicknesses of alumina disk and un-slotted PPS part. The curves and dots are simulated and experimental results, respectively.

Fig. 7. Equivalent circuit model.

other essential indicator is the force factor, deﬁned as the ratio of
the current i to the circumferential vibration velocity v [23].
3.3. Vibration characteristics
First, through ﬁnite element analysis [software: ANSYS (ver.
16.0, ANSYS Inc., Canonsburg, USA)], we investigated the resonancefrequencies fr of triple-layered vibrators when the alumina disks
and the un-slotted parts of PPS vibrating bodies had different thicknesses. As illustrated in Fig. 6, in the cases of the vibrators with
1-mm-thick un-slotted parts, the resonance frequencies increased
from 16 to 25 kHz as the ceramic disk thicknesses increased from
1 to 3 mm because of the increased bending stiffness. When thealumina disk was sufﬁciently thick (>3 mm), the vibrators dominantly exhibited bending vibrations along the r axis instead of thez axis, and the resonance frequencies approached the saturated
values because they were dominantly determined by the radial
thicknesses b of the PPS un-slotted parts [14]. Besides, the vibratorswith identical alumina disk thicknesses showed lower resonancefrequencies when the PPS vibrating bodies had thicker un-slottedparts. However, the double-layered vibrators exhibit increases inresonance frequencies as they become thicker [14,24]. Here, a simpliﬁed equivalent circuit model [1,23] is introduced to explain thereason.
As illustrated in Fig. 7, an electrical and a mechanical arm areparallelly connected in this model [1,6]. The electrical arm contains the clamped capacitance Cd , whereas the mechanical arm
consists of three serially connected elements, i.e. the equivalent
stiffness 1/Cm , mass Lm , and damper Rm ; these parameters canbe calculated from admittance characteristics [measured with an

Here, f0 represents the resonance frequency, Q denotes the mechanical quality factor (Q=f0 /fr , where fr represents the bandwidthcorresponding to 0.707 times of the maximal vibration amplitude),
and Ym0 is the motional admittance. The clamped capacitanceequals Ynr /ωnr , where Ynr and ωnr represent the variationsin admittance and angular frequency, respectively, in the nonresonant portion of an admittance curve. Table 2 lists the equivalentcircuit parameters of the vibrators with s = 1 mm and t = 1 mm (s1t1)
as well as s = 1 mm and t = 3 mm (s1t3). The equivalent mass of the
s1t3 vibrator is 4 times the value of the s1t1 vibrator because thes1t3 vibrator is thicker. Whereas the equivalent stiffness is twice
higher for the s1t3 vibrator than for the s1t1 vibrator. Since thedensity difference is not large between alumina and PPS, and in themeantime, the un-slotted parts of the PPS vibrating bodies havethe thicknesses comparable to the alumina disks, the equivalentmass dominantly depends on their thicknesses. The variation in theequivalent stiffness should be smaller than the change in the equivalent mass because the difference in the elastic moduli between
alumina and PPS is larger than that in the densities. In contrast, thedouble-layered vibrators have increasing resonance frequencies
dominantly because their stiffness becomes higher with increasing
thickness [14].
Subsequently, we discussed how the elliptical motion shape andthe force factor depend on the thicknesses of each layer. Fig. 8(a)demonstrates that the ratios v /vz have negligibly small variations, while the ratios vr /vz exhibit observable variations as thealumina disks became thicker. For instance, the ratios vr /vz of thevibrators with 1-mm-thick PPS un-slotted parts increased gradually in the ranges of 0.5–2.0 mm and 3.5–5.0 mm. However, it
sharply increased from 1.0 to 2.5 when the alumina disk thicknesses
increased from 2.0 to 3.5 mm. It is assumed to originate from theaforementioned change in the dominant vibration modes. Fig. 8(b)illustrates the variations in force factors against the alumina disk
thickness. The vibrators with 1-, 2-, and 3-mm-thick un-slottedparts provided the maximal force factors when the alumina disks
had the thicknesses of 0.8, 1.7, and 2.2 mm, respectively. Whereas
the force factors of the double-layered vibrators with practical
thicknesses (<10 mm) exhibited monotonous enhancements withincreasing thickness [14]. This difference can be explained on thebasis of the positions of neutral axes on the cross-sections of vibrators.
3.4. Neutral axis
Fig. 9(a) shows a simpliﬁed model for calculating the neutral
position. The -axis vibration velocity equals zero at the neutral
position, and increases proportionally to the distance from the neutral position [24]. The neutral axis locates (i) in the PZT disk, (ii) atthe boundary between the PZT and alumina disks, and (iii) in thealumina disk when the vibrators have thick, moderate, and thinalumina disks, respectively. In the cases (i) and (iii), the neutral
positions zN can be respectively obtained by solving the following
equations [24]:162

J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

Table 2Equivalent circuit parameters of s1t1 and s1t3 vibrators.
Vibrator

Clamped capacitance, Cd /×10−12 F

Equivalent mass, Lm /H

Equivalent stiffness, 1/Cm /×1012 F−1

Equivalent damper, Rm /×103

s1t1
s1t3

6.94
6.89

43.8
158.1

0.435
0.974

15.0
38.7

Fig. 8. (a) Ratios v /vz and vr /vz and (b) force factors of the vibrators with different thicknesses of alumina disks and un-slotted PPS parts. The curves and dots are simulated
and experimental results, respectively.

Fig. 9. (a) Neutral positions on the vibrators with (i) thin, (ii) moderate, and (iii) thick alumina disks. (b) Ratios zN /Tt and p/Tt , and force factors of the vibrators with 1-mmthick un-slotted parts. (c) Force factors of the triple-layered vibrators. Here, t1, t3, t8, and t10 represent the PPS/PZT double-layered vibrators with 1-, 3-, 8-, and 10-mm-thickun-slotted parts, respectively.

J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

 p−zN +s+t+h

 p−zN +s
zdS + EAlu

E PPS
p−zN +s p−zNzdS + EPCE 0
zdS + EPCE

zdS = 0
−zN

0

p−zN

(10)

and

 s+p−zN +t+h

 s+p−zN
zdS + EAlu

EPPS
s+p−zN 0
zdS + EAlu0

 p−zNzdS + EPCE

p−zN

zdS = 0,−zN

(11)where EPPS , EAlu , and EPCE denote the elastic moduli of PPS, alumina, and PZT (c11 = 131 GPa), respectively, and dS represents anelementary area (=b·dz). The force factor can be estimated as [25]⎧ e S  2z − p 
N
31 e

 ⎪
⎨ p ·  Tt − zN  when zN ≤ p
e31 Se  v−1 − v−2 
,
·
Af =
 = ⎪ e S  p 
pv−0
⎩ 31 e ·  when zN > pp

Tt − zN(12)

where v -0 , v -1 , and v -2 are respectively the -axis vibration
velocities at the upper surface of the PPS vibrating body, and theupper and bottom surfaces of the PZT disk; Tt is the total thickness (=h+t+s+p); Se is the electrode area; and e31 is the piezoelectric
coefﬁcient.
Fig. 9(b) plots the ratios zN /Tt and p/Tt , and the force factor asfunctions of the alumina disk thickness when the PPS vibrating

163

body has a 1-mm-thick un-slotted part. When the neutral position
locates on the PZT disk, its position advances upwards along thez axis. The force factor becomes higher because the alumina disk
exhibits higher stiffness. It reaches the maximal value when theneutral axis is close to the boundary between the PZT and alumina
disks. Fig. 9(c) illustrates the force factors of other triple-layered
vibrators. Clearly, they have almost the same tendencies with theresults shown in Fig. 8(b); this validates the effectiveness of thismodel. The PPS/PZT double-layered vibrators exhibit their neutral
axes in PZT disks [similar to the case (a) for triple-layered ones]
owing to the relatively high elastic moduli of PZT compared topolymers. Their force factors increase as the PPS vibrating bodies become thicker. It is predictable that double-layered vibrators
provide their maximal force factor when their PPS vibrating bodies have sufﬁcient thicknesses. But in the meantime, there exist
high vibration components in the radial directions, leading to highfrictional loss on the contact surfaces and consequently low performance of motors [14]. Fig. 9(c) also demonstrates that, for the
double-layered vibrators applicable to USM (<10 mm), the force
factors are lower than the values of the triple-layered vibrators.
4. Motor performance
4.1. Experimental setup
Using the transient method [26], we measured the load characteristics of motors with varying geometrical shapes. Fig. 10(a)Fig. 10. (a) Testbed for evaluating motor performance and (b) method of measuring rotation speeds [14,15].

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J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

Fig. 11. (a) Transient response (grey curve) of rotation speed and its exponential ﬁtting curve (black curve). (b) Load characteristics of the s1t3 motor at 65 V (For interpretationof the references to colour in this ﬁgure legend, the reader is referred to the web version of this article).

Fig. 12. Performance of the s1t3 motor as functions of driving voltages under different preloads: (a) Maximum torque, (b) maximum no-load angular velocity, and (c)maximum output power.

depicts the testbed repeatedly used in our previous studies [14,15]:
The vibrator was clamped to a shaft ﬁxed to a stainless-steel baseplate. A pivot bearing composed of a conical head and a dent, ofwhich the cone angles were respectively 55◦ and 60◦ , was employed
to lower the frictional loss. The upper shaft of the bearing wasinserted into a sleeve made of Teﬂon, and the dent was ﬁxed at
the center of the rotor. The preload was adjusted by changing theweights applied to the shaft. The transient responses of rotation
speeds were measured with two laser Doppler vibrometers: As
shown in Fig. 10(b), two beams illuminated the same point on theouter surface of the rotor with the same angles. The rotation speed
was obtained from the outputs of these two vibrometers based ona simple geometry [27].

4.2. Case study
Fig. 11(a) showed the transient response of the s1t3 motor
when a voltage of 65 V and a preload of 0.9 N were applied. The
rotation speed initially exhibited a rapid increase, and at 60 ms,
it approached the saturated value of 1.02 rad/s. Since the transient response included high-frequency ﬂuctuations caused by theultrasonic vibration components, it was ﬁtted with an exponentialfunction:ϕ (t) = ϕmax · [1 − exp (−˛t)] ,(13)

J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

165

Fig. 13. (a) Maximum torques, (b) maximum no-load rotation speeds, and (c) maximum output powers of the motors with different thicknesses of alumina disks andun-slotted PPS parts at 250 V and electromechanical coupling factors of the vibrators. The curves in (a) and (b) xare simulated results, while those in (c) are ﬁtting curves.

where ϕmax and 1/˛ represent the saturated rotation speed and risetime, respectively [25]. The instantaneous output torque and power
are expressed as
T (t) = J ·d [ϕ (t)]dt(14)

d [ϕ (t)]· ϕ (t) ,
dt

(15)

and
P (t) = J ·respectively, where J denotes the moment of inertia of the ﬂywheel and equals 1.24 × 10−5 kg m2 . By deleting the time, therotation speed and output power are presented versus the torque.
Fig. 11(b) plots the results. The motor yielded its maximum torqueof 0.934 mN m when the rotor started to rotate. At a moderate torque, the motor yielded the maximum output power of
0.239 mW.
Fig. 12(a)–(c) respectively demonstrate the maximum torque,
no-load rotation speed, and output power of the s1t3 motor asfunctions of the driving voltage at different preloads. Dead regionsin the torque and no-load speed existed when a low voltage wasapplied. Initially, the output torque increased proportionally to thevoltage, and saturated at a high voltage because it was limited by
the frictional force [25]. The rotation speed increased as the voltage became higher. The maximum output power of 3.4 mW was
obtained at 250 V with the preload of 5.4 N.
4.3. Load characteristics of motors with varying dimensions
Fig. 13 shows the load characteristics of tested motors asfunctions of the thicknesses of their alumina disks and the PPS unslotted parts. The applied voltages were set to 250 V. As plotted inFig. 13(a), the maximum torques of the motors with the 1-mmthick PPS un-slotted parts monotonously decreased from 15 to
2 mN·m as the thickness of alumina disk increased from 1 to 5 mm.

However, among the motors with the 3-mm-thick PPS un-slottedparts, the one with the 2-mm-thick alumina disk yielded a relatively high torque. Clearly, the variations in the maximum torques
originates from the changes in the force factors [2,14,28]. Fig. 13(b)illustrates that, because the -axis vibration velocity decreases as
the alumina disk becomes thicker, there exists a reduction in the
maximum no-load rotation speed [1,2]. As shown in Fig. 13(c), theelectromechanical coupling factor becomes lower with increasing
thickness, and leads to the reduction in output power [29]. It is
worth mentioning that the s5t1 and s5t3 motors have lower output
powers than the s4t1 and s4t3 ones though they have higher electromechanical coupling factors because the negative effects caused
by undesirable vibration components offset the positive effects
caused by the enhancements in the electromechanical coupling
factors [14]. Besides, in the cases of the s5t1 and s5t3 vibrators,
bending vibration are dominantly excited on the slotted parts of
PPS vibrating bodies rather than the un-slotted parts and alumina
disks because the slotted parts have lower bending stiffness [15];this is assumed to result in the relatively high electromechanicalcoupling factors of the s5t1 and s5t3 motors compared to those of
the s4t1 and s4t3 motors.
Table 3 compares the performance of motors with
PPS/alumina/PZT triple-layered vibrators with those with PPS/PZT
double-layered vibrators [14]. The maximum torque of the s1t1
motor is 5 times higher than the value of the PPS/PZT motor
owing to not only the enhancement in force factors but also the
reduction in undesirable vibration components (represented by
vr /vz ). More importantly, the maximal thickness is lower for the
triple-layered than the double-layered vibrators. The s1t1 motor
yields a maximum output power of 39.4 mW, which exceeds 13
times the value of the PPS/PZT motor. Since alumina has lower
damper coefﬁcients than polymers, the triple-layered vibrator
provides lower mechanical loss (represented as the equivalent
damper), which possibly leads to a higher efﬁciency for the s1t1

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J. Wu et al. / Sensors and Actuators A 284 (2018) 158–167

Table 3Comparison in performance of USMs with PPS/alumina/PZT triple-layered and PPS/PZT double-layered vibrators.
Performance

USM with triple-layered vibrator

USM with double-layered vibrator

Maximum output torque at 250 V/mNm
Optimal thickness corresponding to maximum output torque/mm
Force factor/N·V−1
Ratio vr /vz
Maximum no-load rotation speed at 250 V/rad s−1
Optimal thickness corresponding to maximum no-load rotation speed/mm
Maximum output power at 250 V/mW
Optimal thickness corresponding to maximum output power/mm
Electromechanical coupling factor/%
Maximum efﬁciency/%
Equivalent damper/×103
Maximum power density/W kg−1

15.2
2 (s = 1 mm, t = 1 mm)
0.4
0.9
8.9
2
39.1
2
7.9
8.3
15.0
10.3

2.9
8
0.1
2.5
16.1
2
3.0
2
0.4
4.8
45.0
2.5

motor than for the double-layered motor. Besides, the weightof the triple-layered motor slightly increases compared to the
double-layered one owing to the moderate density of alumina andlow thickness of the disk; this causes a higher power density of the
PPS/alumina/PZT triple-layered motor.
5. Conclusions
In this study, we developed a PPS/alumina/PZT triple-layered
vibrator as a core component of USM. After discussing the vibration
characteristics of vibrators and measuring the load characteristics
of motors, we have drawn the following conclusions:(1) The PPS/alumina/PZT triple-layered vibrator exhibited the
maximum force factor when its neutral axis was close to theboundary between the PZT and alumina disks.
(2) Relatively high output torque and power were obtained on the
triple-layered motor with the smallest thickness.
(3) The triple-layered motor exhibited the maximum output
torque and power of 15.2 mN m and 39.3 mW, respectively 5
and 13 times the values achieved on our previously reported
double-layered motors.
We have gained an understanding on the triple-layered motors
and anticipate that the obtained results will provide adequate
information for further optimization. To achieve the practical applications in chemical industry, the accessory components of motors,
e.g. feeding lines and bearings, will be carefully selected or speciallydesigned in the future.
Acknowledgement
The authors thank the staffs with the Precision and Manufacturing Center, Technical Department, Tokyo Institute of Technology,
for machining the motor components. This work was supportedby the Japan Society for the Promotion of Science (JSPS) KAKENHI
Grant Number 17J05057. JSPS KAKENHI Grant Number 17J05057.
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Biographies

Jiang Wu was born in Liaoning, China, on January 29,
1988. He received the B.E. degree in mechanical engineering from Dalian University of Technology, China, in2010. From 2010 to 2012, he studied in the State Key
Laboratory of Robotics and System, Harbin Institute ofTechnology (HIT), China, and received the M.E. degree inmechatronic engineering from HIT in 2012. From 2012 to2017, he studied in the Future Interdisciplinary Researchof Science and Technology, Tokyo Institute of Technology(TITECH), Japan, and received Dr.Eng. degree in electrical and electronic engineering from TITECH in 2017. His
research interest includes piezoresistive and piezoelectricmaterials, permanent-magnet-based sensing technology,
and polymer-based ultrasonic transducers and actuators.
Yosuke Mizuno received the B.E., M.E., and Dr.Eng.
degrees in electronic engineering from the Universityof Tokyo, Japan, in 2005, 2007, and 2010, respectively.
From 2007 to 2010, he was involved in Brillouin opticalcorrelation-domain reﬂectometry for his Dr.Eng. degree
at the University of Tokyo. From 2007 to 2010, he was a
Research Fellow (DC1) of the Japan Society for the Promotion of Science (JSPS). From 2010 to 2012, as a Research
Fellow (PD) of JSPS, he worked on polymer optics at
Tokyo Institute of Technology, Japan. In 2011, he stayedat BAM Federal Institute for Materials Research and Testing, Germany, as a Visiting Research Associate. Since 2012,167

he has been an Assistant Professor in the Precision andIntelligence Laboratory (presently, Institute of Innovative Research), Tokyo Institute of Technology, where he is active in ﬁber-optic sensing, polymer optics, andultrasonics. Dr. Mizuno is the winner of the Ando Incentive Prize for the Study ofElectronics 2011, the Konica Minolta Imaging Science Award 2014, the JapaneseSociety of Applied Physics (JSAP) Young Scientist Presentation Award 2015, and the
Optical Society of Japan (OSJ) Optics Paper Award 2017, the Optical Design Award2018. He is a Senior Member of the IEEE Photonics Society and a member of the JSAP,
the OSJ, and the Institute of Electronics, Information, and Communication Engineersof Japan.
Kentaro Nakamura was born in Tokyo, Japan, on July 3,
1963. He received the B.E., M.E., and Dr.Eng. degrees from
Tokyo Institute of Technology, Japan, in 1987, 1989, and1992, respectively. Since 2010, he has been a Professor
at the Precision and Intelligence Laboratory (presently,
Institute of Innovative Research), Tokyo Institute of Technology. His research ﬁeld is the applications of ultrasonicwaves, measurement of vibration and sound using optical methods, and ﬁber-optic sensing. Prof. Nakamura is
the winner of the Awaya Kiyoshi Award for Encouragement of Research from the Acoustical Society of Japan(ASJ) in 1996, and the Best Paper Awards from the Instituteof Electronics, Information and Communication Engineers(IEICE) of Japan in 1998 and from the Symposium on Ultrasonic Electronics in 2007
and 2011. He also received the Japanese Journal of Applied Physics Editorial Contribution Award from the Japan Society of Applied Physics (JSAP) in 2007 and the
Optical Design Award 2018. He is a member of the IEEE, the ASJ, the JSAP, the IEICE,
and the Institute of Electrical Engineers of Japan. He served as the president of ASJ
from 2015 to 2017.